Apply the special theory of relativity to prove that the time interval t in themoving reference frame S' appears to be longer by a factor 1//1–z to theobserver in the stationary frame S. [CO3]

Consider that you are in an inertial frame (S) where there is a light clock consisting of 2 mirrors…

Answered: Apply the special theory of relativity…

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter39: Relativity

Section: Chapter Questions

Problem 19PQ

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A yet-to-be-built spacecraft starts from Earth moving at constant speed to the yet-to-be-discovered planet Retah, which is 20 lighthours away from Earth. It takes 25 h (according to an Earth observer) for a spacecraft to reach this planet. Assuming that the clocks are synchronized at the beginning of the journey, compare the time elapsed in the spacecraft’s frame for this one-way journey with the time elapsed as measured by an Earth-based clock.
Suppose our Sun is about to explode. In an effort to escape, we depart in a spaceship at v = 0.80c and head toward the star Tau Ceti, 12 lightyears away. When we reach the midpoint of our journey from the Earth, we see our Sun explode and, unfortunately, at the same instant we see Tau Ceti explode as well. (a) In the spaceship’s frame of reference, should we conclude that the two explosions occurred simultaneously? If not, which occurred first? (b) In a frame of reference in which the Sun and Tau Ceti are at rest, did they explode simultaneously? If not, which exploded first?
The proper length of one spaceship is three times that of another. The two spaceships are traveling in the same direction and, while both are passing overhead, an Earth observer measures the two spaceships to have the same length. If the slower spaceship has a speed of 0.350c with respect to Earth, determine the speed of the faster spaceship.
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Suppose our Sun is about to explode. In an effort to escape, we depart in a spacecraft at v = 0.800c and head toward the star Tau Ceti, 12.0 ly away. When we reach the midpoint of our journey from the Earth, we see our Sun explode, and, unfortunately, at the same instant, we see Tau Ceti explode as well. (a) In the spacecrafts frame of reference, should we conclude that the two explosions occurred simultaneously? If not, which occurred first? (b) What If? In a frame of reference in which the Sun and Tau Ceti are at rest, did they explode simultaneously? If not, which exploded first?
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An alien spaceship traveling at 0.600c toward the Earth launches a landing craft. The landing craft travels in the same direction with a speed of 0.800r relative to the mother ship. As measured on the Earth, the spaceship is 0.200 ly from the Earth when the landing craft is launched, (a) What speed do the Earth-based observers measure for the approaching landing craft? What is the distance to the Earth at the moment of the landing craft's launch as measured by the aliens? What travel time is required for the landing craft to reach the Earth as measured by the aliens on the mother ship? (d) If' the landing craft has a mass of 4.00 10s kg. what is its kinetic energy as measured in the Earth reference frame?
The proper length of one spaceship is three times that of another. The two spaceships are traveling in the same direction and, while both are passing overhead, an Earth observer measures the two spaceships to have the same length. If the slower spaceship has a speed of 0.350c with respect to Earth, determine the speed of the faster spaceship.
Recall, from this chapter, that the factor gamma (γ) governs both time dilation and length contraction, where When you multiply the time in a moving frame by γ, you get the longer (dilated) time in your fixed fame. When you divide the length in a moving frame by γ, you get the shorter (contracted) length in your fixed frame. Pretend that the starship in the problem 1 is somehow traveling at c with respect to Earth and it fires a drone forward at speed c with respect to itself. Use the equation for the relativistic addition of velocities to show that the speed of the drone with respect to Earth is still c. problem1 Recall, from this chapter, that the factor gamma (γ) governs both time dilation and length contraction, where When you multiply the time in a moving frame by γ, you get the longer (dilated) time in your fixed fame. When you divide the length in a moving frame by γ, you get the shorter (contracted) length in your fixed frame. A starship passes Earth at 80% of the speed of…

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Apply the special theory of relativity to prove that the time interval t in the moving reference frame S' appears to be longer by a factor 1//1– z to the observer in the stationary frame S. [CO3]